Another Conservative woman is going to be Britain’s prime minister. The bookies think it will be Theresa May, the home secretary for a record-breaking six years. But no one’s quite ready to rule out the other name on the ballot paper: Andrea Leadsom. Leaving out the joke that her CV says she’s already prime minister, she is a committed Brexiter, and the selectorate in the wider Conservative party may think she – as the Daily Telegraph argues – is the woman who could give the Tory right the chance to take their party back.

There are two reasons why this is an entirely unprecedented turn of events. First, because no British prime minister has ever been chosen by a party’s members. Second, because no party has ever chosen between two women for leader, let alone prime minister. There is a PhD thesis to be written on why the party of tradition can make space for women, while UK-wide parties of the centre and the left (except the Greens) have still not elected a female leader, let alone a prime minister.

Next PM to be woman as Theresa May and Andrea Leadsom win MPs' vote

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Women in prominent positions in the UK are still so unusual that Margaret Thatcher remains the archetype, at least on the right, although the German chancellor, Angela Merkel, may have some influence. Whichever model, women in politics, however unfairly, still have to make a decision about how to handle the gender thing, and generally they do it more like Merkel than like Thatcher – by pretending it doesn’t exist. The days when the Northern Ireland secretary Mo Mowlam sent her detective out to buy tampons seem long distant.

Some male politicians have found it necessary to explain that they are quite happy to have a choice between two women, as long as they were on either side of the Brexit divide. For those still struggling, the men’s magazine GQ has helpfully framed the choice in the context of the two mummies: the one who makes you do your homework (May), and the one who’ll let you have ice-cream for breakfast (Leadsom).

May, whose political brand is caution, has trodden a typically judicious line on gender. She exploited her femininity with a penchant for sassy shoes back in the days when she was chair of the party, and she occasionally wears striking dresses, like the black one with the contrasting zip from neck to hem at the back that she wore at the party conference last year – but she wore it while delivering a speech that was so hardline on migration that even some cabinet colleagues disowned it.

She was, after all, the overseer, if not the instigator, of the “Go Home” billboards of 2013, and the creator of the tale of the migrant recounted in another of her party conference speeches: he had allegedly ducked deportation because the court accepted that he had a family life with a cat, and so deportation would breach his human rights (another story flatly denied by colleagues).

Her first move after the referendum result was to declare that she accepted it. Her second was to indicate that she would drop her long hostility to the European convention on human rights.

On the other hand, she has made domestic violence a priority, and won the admiration of colleagues, and even the respect of families, in the way she backed the Hillsborough inquest and ensured equivalence of funding between the families and the police. While she initially mishandled allegations of a coverup of high-level child abuse, she has now set up a serious inquiry; and she won plaudits from campaigners for the sympathetic and determined way she is tackling deaths in custody.

May has a reputation for being too focused on her brief and not broad enough in her interests, a charge sometimes made by men generalising about women. But she also has a useful reputation for not minding whether or not people like her. That is probably why Kenneth Clarke, in his on-mike ramble through the virtues of the leadership candidates, called her a “bloody difficult woman”, a description she has been quick to capitalise on (and which will do her no harm at all).

Leadsom, who has only been an MP since 2010, has less of a track record. Her work with the charity PIP, which she set up to promote early-years care and the importance of bonding between mother and child, is, in the mirror-glass world of gender politics, capable of being interpreted as a feminist gesture. But it is also part of a traditional rightwing concern for family life which still thinks mothers belong at home.

Maybe the most interesting observation about politics through the prism of gender comes from Germany, where the talk is increasingly of women coming in to clear up the mess left by men. Merkel earned that badge when she inherited a party badly damaged by a funding scandal. Nicola Sturgeon and other Scottish political leaders, in particular Ruth Davidson, the Tory leader, have added to the impression that women are reaching the voters men don’t. Now the Tory party – and who knows, maybe, at last, Labour too – is going to add to the new force of Femokratie.